SECTIONAL TRANSACTIONS.— A. 341 



In the first term, w=»io/(l— «Vc^)*» where wio=feV'* ^nd account is taken of the 

 boundary stresses (probably magnetic in origin) which keep the electron in equi 

 librium. The eleetrodynamic moments of inertia may be rigorously evaluated for 

 the simple type of spinning electron considered, and in general may be expressed in 

 powers of ^'^=v^/c- in the form 



A=I(H-a,pH«2P<+ • •). B=C=I(l+Cip2+C2(5^+ . . .) . . (T. 



where /=Jj?7o'*^ is the moment of inertia of the spinning electron at rest. Applying 

 Lagrange's equations to the rotations expressed by T as kinetic energy, the precessional 

 motion of the electron is determined by Euler's equations, 



Aico=Li C(i>2 — (C — A)oic08=Lo — C^W2 1 rQ« 



Cco;,+(C-A)caiCo,=L3-Ci-w3 J • • • • ^-^^ 



(LjLaLs) being couples from nuclei in atomic systems, or due to the magnetic forces 

 of the radiation field. The processing electron has magnetic moments proportional 

 to (wiWoM.s) whose periodic variations thus give rise to electro-magnetic radiation of 

 the same frequency. The constant A; is a simple type of damping factor due to the 

 loss of rotational energy by radiation. Under no forces the stable configuration of 

 the electron is easily seen from (.3) to be with the axis of spin along the direction of 

 motion. When disturbed the frequency of precessional motion and of emitted radia- 

 tion is seen to be, if Qi is the intrinsic spin, 



27rv=ai(C-A)/C=a(ci-«i)P''(l+6ipH&2(3^+ • • • ) ... (4) 

 If we denote 



hCli=TZc'^mo/(ci — o,) (5) 



where (ci — aj) is a numerical constant equal to f for the simple model considered, 

 we have to a first approximation a relation between precessional electron radiation 

 and velocity in the form 



Av=imov2 (6) 



the well-known photo-electric equation, while Planch's constant h becomes a fundamental 

 characteristic of a rotating electron ex-pressed in terms of spin by equation (5). 



This purely classical interpretation appears to be the kej- to radiation problems 

 generally. With similar hypotheses as to spinning protons as constituents of atomic 

 nuclei, the theory of slightly perturbed, simple orbits under an inverse-square law of 

 «lectrostatic attraction from the nucleus, with the fundamental relations (6), leads to 

 the series formula for hydrogen and helium spectra and in more complex cases to the 

 S, P, D and F series, with the correct value for the Rydberg constant. Perturbations 

 of orbits due to variation of mass with velocitj', external electric and magnetic fields, 

 with in some cases slightly different interpretations, lead to formulae the correct type 

 for fine structure, Zeeman (normal and anomalous) and Stark effects. The funda- 

 mental formula (6), used in conjunction with a Maxwellian distribution of electron 

 velocities, also leads with reasonable hypotheses as to electron orbits in a space lattice 

 to Planck's formula for black-body radiation and the associated formulae for specific 

 heats. 



26. Dr. S. G. Bakker, Mr. A. T. King, and Mr. H. R. Hirst.— T^t 

 Hygroscopic Relations of Colloidal Fibres, with Special Referetice 

 to their Industrial Importance. 



The theory of elasticity of colloidal fibres is developed, and it is shown that wool 

 fibres follow the usual characteristics of colloids. There is apparently an elastic 

 framework filled with a viscous medium. The effect of moisture absorption on the 

 viscous phase is discussed, and it is found that wool is a perfectly elastic material 

 and makes a complete recovery from strain even up to its breaking point. The effect 

 of moisture on thermal and electrical conductivity is discussed. In the former case 

 it is shown that the increase in thermal conductivity of any material for an increase 

 of moisture content of 1 per cent, of the dry weight ranges from 1.7 to 2.0 x lO'^ for 

 ■wool. 



The electrical conductivity is shown to increase with moisture content, and it is 

 noted that dry fibres are non-conducting. A table of results is given. Section II 

 treats of the variation of density, swelling, and heat of wetting of wool, and from the 

 results a theory of wool structure is put forward. Tables are given for density measure- 

 Tnents and heat evolved upon wetting at various humidities. 



